CCO '11 P4 - Reorganization

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Points: 15 (partial)
Time limit: 1.0s
Memory limit: 256M

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Canadian Computing Competition: 2011 Stage 2, Day 2, Problem 1

Alice and Bob own a huge company. This company was losing money consistently over the last 30 years, since its owners spent too much time playing games with mathematicians. Alice and Bob decide to make a change.

Alice and Bob start by giving unique employee IDs to each of the n employees (1 \le n \le 100\,000), where each ID I is in the range (1 \le I \le 100\,000).

Then, Alice and Bob give unique ranks to each employee. Each rank R is an integer such that 1 \le R \le 10\,000\,000. After this, they plan to reorganize the company, by making sure that the employees satisfy the following conditions:

  1. There is exactly one director, who has no supervisor;
  2. Except for the director, each employee has a supervisor, and this supervisor has a smaller employee ID and a higher rank (the value of rank is smaller); and
  3. Each employee can supervise at most 2 people.

Alice and Bob are eager to know whether their company can be reorganized successfully.

Input Specification

The input is a total of 2 lines. The first line contains n (1 \le n \le 100\,000), indicating the number of employees. The next line contains n distinct integers R (1 \le R \le 10\,000\,000), where the ith integer indicates the rank of the employee with ID i.

Output Specification

Output YES if the company can be reorganized successfully; output NO otherwise.

Sample Input 1

6
1 6 5 2 3 4

Output for Sample Input 1

NO
Explanation for Output for Sample Input 1

Employee with rank 1 has employee ID 1, and thus, must be the supervisor. Employees 2 and 3 (with ranks 6 and 5) can only be supervised by employee 1 (with rank 1). However, no other employee (4, 5 or 6) can be supervised by employee 2 or employee 3, since ranks of supervisors must be smaller than the employees they supervise.

Sample Input 2

6
1 6 2 3 4 5

Output for Sample Input 2

YES
Explanation for Output for Sample Input 2

Employee 1 (rank 1) supervises both employee 2 (rank 6) and employee 3 (rank 2).

Employee 3 (rank 2) supervises employee 4 (rank 3) and employee 5 (rank 4).

Employee 4 (rank 3) supervises employee 6 (rank 5).


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